Charged particles in aqueous suspension form an electrical double layer at their surfaces, which plays a key role in suspension properties. For example, binder particles in latex paint remain suspended in the can because of repulsive forces between overlapping double layers. Existing models of the double layer assume sharp interfaces bearing fixed uniform charge, and so cannot describe aqueous binder particle surfaces, which are soft and diffuse, and bear mobile charge from ionic surfactants as well as grafted multivalent oligomers. To treat this industrially important system, we use atomistic molecular dynamics simulations to investigate a structurally realistic model of commercial binder particle surfaces, informed by extensive characterization of particle synthesis and surface properties. We determine the interfacial profiles of polymer, water, bound and free ions, from which the charge density and electrostatic potential can be calculated. We extend the traditional definitions of the inner and outer Helmholtz planes to our diffuse interfaces. Beyond the Stern layer, the simulated electrostatic potential is well described by the Poisson-Boltzmann equation. The potential at the outer Helmholtz plane compares well to the experimental zeta potential. We compare particle surfaces bearing two types of charge groups, ionic surfactant and multivalent oligomers, with and without added salt. Although the bare charge density of a surface bearing multivalent oligomers is much higher than that of a surfactant-bearing surface at realistic coverage, greater counterion condensation leads to similar zeta potentials for the two systems.